System for locating errors in calculations.



J. C. PETTIT. SYSTEM P011 LOGATING ERRORS 1N GALGULATIONS.

' APPLIUATION FILED SEPT. 3, 1910.

Patented Aug. 8, 1911.

JAMES CUTHBERT PETTIT,

OF CREVVE, VIRGNIA.

SYSTEM FOR LOCATING ERRORS IN CALCULATXONS.

To all whom it may concern:

Be it known that I, JAMES CUTHBERT PET- 'rrr, a citizen of the United States, residing at Crewe, in the county of Nottoway and State of Virginia, have invented a new and useful System for Locating Errors in Calculations; and l do hereby declare t-he following to be a full, clear, and exact description of the invention, such as will enable others skilled in the art to which it appertains to make and use the same.

This invention belongs to the art of mathematical calculating, and it particularly relates to a new and useful system for locating errors in calculations, and the primary object of the invention is to provide such a system in which there is involved various novel characteristics.

It is a well known fact, among clerks in their various callings, for instance bookkeeping and other clerical work, drafting, and engineering, that the majority of errors in calculating result from the transposition of figures (which are transposable) and it is a further fact that heretofore these errors have been exceedingly difficult to trace or locate more than any other class of errors. Moreover, it is well known and a regular occurrence, that an error of 9 or a multiple of 9 results from a transposition.

The fundamental object of this system is to facilitate the finding and the location of the error of transposition, in order that it may be immediately corrected. It is evident, however, that a system of this character saves time, labor and considerable thought. To locate or find an error of 9 (which may result from the transposition of 1 to 10 or vice versa, or from 12 to 21 or vice versa, and on through a series of numbers upto 89 and 98, in which there is a difference of 9), you will find the transposed number in column one, at the top of which the numeral 9 is indicated. To find an error of a multiple of 9, say for instance 18 or 27, you will ind the transposed number in column two or three. The numbers consecutively arranged in any one of the columns shown in the drawings have a dilference of 9 or a multiple thereof, and by these columns of numbers one may ascertain the transposed number.

ln the drawings there is only disclosed Specification of Letters Patent.

Application led September 3, 1910.

Patented AuO. 8, 11911.

Serial No. 580,366.

one arrangement of numbers, but in practical elds this arrangement may be varied, and provided the varied arrangement is comprehended by the claim, the applicant is entitled to it.

Cther features Vand combination of parts will hereinafter appear throughout the specilication, and shown in the drawings and claims. In the drawings, however, there is disclosed a chart, upon which columns of various transposable numbers are arranged, with full directions arranged above the columns, in order that one may ascertain the use of this system.

Referring to the drawings 1 denotes a chart which may be made of any suitable card-board or other material, upon which is drawn a square outlined space 2. This space is divided in order to provide 81 square outlined spaces 3. By providing these spaces 3 vertical and horizontal columns are formed. The vertical columns are designated by the numerals 4, 5,6,7, 8,9, 10, 11 and 12, it being understood, however, that column 4 is the first column, while the others are the second, third and fourth columns, etc., up to the ninth which is designated by 12. Column 4 contains various numbers, the differences between them being 9. Column 5 has a plurality of numbers, which may be transposed to obtain a difl'erence of a multiple of 9, for example 18. The other columns from 6 to 12 inclusive have arranged therein. various numbers, the differences between which are also a multiple of 9, for example, 27, 36, 45, 54, 68, 72 and 81. These numbers 27, 86, 45, 54, 68, 72, and 81 are designated by the character 13. Below each column the transpositions of the differences between the numbers in the columns below the line 14 are indicated, and are denoted by the character 15. These numbers 15 when transposed read 90, 81, 7 2, 63, 54, 45, 36, 27, and 18. The blank spaces 16 may be used for other transposable numbers, say for example, numbers above 100. The transposition of numbers above 100, occur generally in the last two figures, such as the transposition of 101 to 110 or 112 to 121, the differences between which are 9; or such as the transposition of 102 to 120, or 103 to 130, or 113 to 131. It will be noted, that by the transposition of these last mentioned numbers, the result would be a multiple of 9, such as 18 and 27. It is evident, however, that the present invention is not to be confined to the special arrangement, as shown in the drawings; it is to be granted that the transposable numbers may be increased in denomination, and arranged upon the chart in any desirable manner. Furthermore, the chart may be varied in design and contour; moreover, the directions 17 and other data 18, at the top and bottom of the chart, may be added to or condensed, in order to facilitate the use of this system.

As a commercial proposition this system affords an excellent medium, as an advertiser, and in practical fields it is found to be indispensable. 1t is to be remembered, that the owners of the rights in this invention may, as an inducement, advertise banks or other business houses upon the backs or the margin of the charts. That is to say, when a bank pays for the use of this system, it will receive charts with the advertisements of other business houses upon them, and their advertisements are placed upon other distributed charts, as an indu-cement. By this method, an endless chain of advertising is produced.

A clerk in totaling a column of fig ures consisting of two rows, finds that the result does not agree with the cash, books or other numerical records. The difference or error, is caused by the transposition of a number, the difference between which results in 9 or a multiple thereof. If the error be 18, the clerk necessarily looks in column 5, over which the numeral 18 is disposed, and he will find the number (which has been transposed he is adding in with others in said column 5, by comparing` this column 5 of transposable numbers with the numbers he is adding. In this way one may locate the number which has been transposed.

In a department store or business house when comparing the sum total of the cash with the sum total of the amounts of a plurality of sales itemized in a ledger, it is desired to locate or trace an error, say for instance an error of 18, which is the result of the transposition of a number, it is accomplished in the following manner:

Immediately below two columns of figures are disclosed as follows Amounts of Amount of sales checks. in ledger. $34.00 $34.00

Total- $314.00 Total $296.00

It will be observed that there is a dilference of $18.00 between the suin totals of the checks and the amount of sales in the ledger, as shown by the subtraction of the sum total of the amount of sales from the sum total of the checks as follows:

Sum total of the amount of checks- $314. 00

As a general rule this difference is caused by the transposition of a number, for example, two clerks, one calling out t-lie Iamounts of the checks to the other transposed oiie of the amounts of the checks. The clerk who may be calling the amounts out may dictate one number when he should have said another, or the other clerk in taking the dictation may write one number when he should have written a different one, for instance, as will be observed one number has been written $42 when it should have been $24, as shown in the column of the amount of checks. To locate the transposition of the amount of this particular check, the difference between the sum totals of the checks and amount of sales is learned by the above subtraction, which is $18, and by looking in the column which is designated by the numeral 5 in the drawings, with -18 at the top thereof you will find the numeral 24, which has been transposed to 42 by the clerk when writing the amounts of the checks, as shown above. This system of locating transposed numbers has served an excellent purpose in various business houses, in lesseniiig the work of the cashiers and bookkeepers and bankers. Vithout this system it is necessary to run over columns of figures (in which there may be fifty to a hundred or more numbers) several times before locating the number which has been transposed.

The invention having been set forth, what is claimed as new and useful is 1. A chart having transposable numbers arranged in columns, with the difference between them indicated at the top of each column.

2. A chart having a plurality of columns of transposable numbers arranged in a square, and comparable with columns of figures to be added, said chart having the differences between the transposable numbers arranged at the top of each column.

8. A chart having a plurality of columns of transposable numbers arranged in a square, and comparable with columns of figures to be added, said chart having the differences between the transposable numbers arranged at the top of each column, said differences being 9 or a multiple thereof.

4. A chart having a square outlined space divided into vertical and horizontal columns of squares, with a diagonal line eX- tom of each vert-ical column, as and for the purpose specified.

In testimony whereof I have signed my name to this speciioation in the presence of two subscribing witnesses.

JAMES CUTHBERT PETTIT.

Witnesses WV. D. SHUFFLEBORGER,

P. V. MAY.

Copies of this patent may be obtained for five cents each, by addressing the Commissioner of Patents, Washington, D. C. 

